2D reductions of the equation u yy = u tx + u yu xx − u xu xy and their nonlocal symmetries

We consider the 3D equation $u_{yy} = u_{tx} + u_yu_{xx} - u_xu_{xy}$ and its 2D reductions: (1) (u_y+y)u_{xx}-u_xu_{xy}-2$ (which is equivalent to Gibbons-Tsarev equation) (2) (u_y+2x)u_{xx} (y-u_x)u_{xy} -u_x$. Using reduction of known Lax pair for equation, we describe nonlocal symmetries of~(1) and~(2) show that Lie algebras these are isomorphic Witt algebra.